Question

6. A recent study examined the one-way commute times in the 30 largest cities in the United States. The longest one-way travel time is in New York City, where the mean time is 39.7 minutes. Assume the distribution of travel times in NYC follows the normal distribution and the standard deviation is 7.5 minutes.

(a) What percent of the New York City commutes are for less than 30 minutes? Explain every step of your work. Use the z-table found in Appendix B of your textbook.

(b) What percent of commutes in NYC are between 30 and 35 minutes? Explain every step of your work. Use the z-table found in Appendix B of your textbook.

(c) What percent of commutes are between 30 and 50 minutes? Explain every step of your work. Use the z-table found in Appendix B of your textbook.

Answer 1

Given,

= 39.7 , = 7.5

We convert this to standard normal as

P( X < x) = P( Z < x - / )

a)

P( X < 30) = P( Z < 30 - 39.7 / 75)

= P( Z < -1.2933)

= 0.0980

b)

P( 30 <X < 35) = P( X < 35) - P( X < 30)

= P( Z < 35 - 39.7 / 7.5) - P( Z < 30 - 39.7 / 7.5)

= P( Z < -0.6267) - P( Z < -1.2933)

= 0.2654 - 0.0980

= 0.1674

c)

P( 30 < X < 50) = P( X < 50) - P( X < 30)

= P( Z < 50 - 39.7 / 7.5) - P( Z < 30 - 39.7 / 7.5)

= P( Z < 1.3733) - P( Z < -1.2933)

= 0.9152 - 0.0980

= 0.8172